Bessone moved from Espanyol B to Welsh team Swansea City in June 2008, on a free transfer.[3] On 20 November 2009, Bessone scored his first goal for Swansea in a 1–0 win over League rivals Derby County, helping Swansea climb to third in the Championship, the highest position they had reached in over 26 years.[4]

After the 2009–10 season finished Bessone was offered a new deal at Swansea but turned it down in favour of joining Leeds United; he signed a three-year contract and became their fourth signing of the summer.[5][6]

On 21 January 2011, Bessone moved to Charlton Athletic on a loan deal until the end of the season, with the option of a permanent transfer.[7] In February 2011, Bessone gave an interview to the Yorkshire Evening Post where he admitted his performances for Leeds has been "opened to close scrutiny."[8] In May 2011, Bessone was transfer listed by Leeds United,[9] and he was linked with a move to Charlton.[10] After failing to find a new club, Bessone returned to training with Leeds United in June 2011,[11] and he was later named in their squad for a friendly tour of Scotland.[12]

On 31 August 2011, Bessone had his contract with Leeds cancelled by mutual consent, and he re-joined Swansea that same day,[13] to provide defensive cover for the injured Alan Tate.[14] The transfer was initially delayed while awaiting international clearance from FIFA.[15] Bessone only made one Premier League appearance in his second spell at Swansea, appearing as a late substitute against West Bromwich Albion.[16]

Bessone signed with Oldham Athletic on 28 March 2013 for defensive cover as left back Jonathan Grounds was one yellow card away from a two match ban towards the end of the season.[18] Bessone was released at the end of the season without playing a single game for the club.[19]